1) You can use the NSString UIKit Additions to compute the size taken by the text (and adjust the size of your UITextView accordingly). You may seen an example here.

For example, if you need to know the CGSize that is taken by your NSString if rendered on a single line, use CGSize sz = [_textView.text sizeWithFont:_textView.font] then adjust your frame given this size value.

If you need to know the size taken by your text if rendered on multiple lines, wrapping it if the text reaches a given width, use sizeWithFont:constrainedToSize:lineBreakMode: instead, etc.

2) You may also be interested in the sizeThatFits: and sizeToFit methods of UIView.
The first one returns the CGSize (that fits in the given CGSize passed in parameter) so that your UITextView can display all your text. The second actually do the resizing, adjusting the frame for you.